The present invention relates, in general, to drive systems and, more particularly, to a pedal drive system for imparting a rotational force through linear travel of the pedal.
The conventional bicycle is an example of a device that employs a crank and sprocket drive system. That type drive system utilizes the force supplied by a rider to pedals traveling in circular paths in order to generate rotational motion propelling the bicycle in a forward direction. Typically, bicycles include two opposing rotatingly mounted cranks. The cranks are drivingly connected through a chain to a rear wheel of the bicycle which is in contact with a stationary surface, such as the ground. Pedals are attached to the ends of the cranks. A seat is provided on the bicycle for supporting a rider. A rider may mount the bicycle by positioning himself on the seat of the bicycle and placing his feet on the pedals of the bicycle. To propel the bicycle forward, the rider exerts force through his feet against the pedals, thereby causing the cranks to rotate, and thus creating a torque. The torque is transferred via the chain to the rear wheel, thereby causing the rear wheel to rotate. The friction of the rotating wheel against the stationary surface causes the bicycle to move forward.
A drawback to the foregoing system for propelling a bicycle is that, as the rider imparts force to the pedals of the bicycle, his feet are constrained to move in a circular manner. It can be appreciated that the rider induces, through the cranks, a torque with respect to each pedal and crank that is equal to the product of the force applied to the pedal times the length of the crank perpendicular to that force, i.e., the moment arm. The moment arm is proportional to the leverage, or mechanical advantage, of the bicycle for transmitting force supplied by the rider to the wheels to thereby propel the bicycle.
The forces exertable by a bicyclist on rotating pedals are primarily directed vertically downward. This is the case because both the rider's weight due to gravity and the rider's leg strength due to the human physique create primarily vertically downward directed forces when the rider is positioned on the bicycle. When a crank moving through its circular path of motion is generally horizontal with respect to the surface and continuing downward movement in the circular path, therefore, the moment arm is the entire length of the crank. Hence, the mechanical advantage is maximized when the crank is so positioned. When a crank moving through its circular path of motion is generally vertical with respect to the surface and beginning downward movement in the circular path, (i.e., when the pedal is at the top of the circular path of motion), however, then the moment arm is zero. Hence, the mechanical advantage is minimized when the crank is so positioned. As the respective cranks of the typical bicycle rotate along their circular paths between vertical and horizontal positions, the mechanical advantage ranges between maximum and minimum values directly proportional to the maximum and minimum length of the moment arms.
Unfortunately, the maximum mechanical advantage is achieved only instantaneously (i.e., for less than one degree of rotational travel) as the crank passes through the horizontal position and continues its circular path. As the crank moves from the horizontal position to the vertical position at the bottom of the circular path, the mechanical advantage decreases from maximum to minimum. As the mechanical advantage decreases, the energy exerted by the rider becomes less efficiently utilized. It can be shown, assuming a rider's energy is utilized with 100% efficiency when the cranks in their rotation are horizontal (i.e., because of the rider's weight and strength directed downward), that the average efficiency with which his energy is utilized as he pedals in a circular path is about 64%, as calculated by averaging the sine of each of the 360 degrees of the path of the two cranks. Such inefficient utilization of energy is readily appreciated when the rider attempts to accelerate his bicycle from a stationary position by exerting downwardly directed forces while the cranks are positioned vertically. Similar inefficiency is also observed when a driver accelerates an automobile from a stationary position in a high gear instead of a low gear. Energy is, thus, not efficiently utilized and acceleration and speed maintenance is, thus, greatly impeded.
Therefore, what is needed is a drive system in which a substantially maximum mechanical advantage is sustained, and in which fluctuation of the mechanical advantage is minimized, over the full stroke of the drive system.